Solvability of the Problem of Nonisothermal Filtration in a Thin Poroelastic Layer
УДК 517.95
Abstract
The two-phase filtration problems arise in various fields of human activity, such as oil and gas extraction, snowmelt modeling, and medicine. All these applications require the development of approaches for modeling such processes, creating models, and theoretically substantiating them. There are various approaches to simulate two-phase filtration processes. This article discusses an approach based on the classical Masket — Leverett model, supplemented by equations for the characteristics of a porous medium and temperature. An initial boundary value problem is set for this model. The studied system splits into two subsystems after dimensionalization and formal passing to a limit with a small parameter. One of the subsystems is closed under its unknown functions and equations. The structure of equations allows finding the classic solution for a problem with smooth initial boundary conditions. The problem is complicated by numerous inconsistencies. The study uses various classical methods of differential equations. The novelty of this study is the use of the variable porosity in the problems of non-isothermal two-phase filtration in a thin poroelastic layer.
Downloads
References
Папин А.А., Подладчиков Ю.Ю. Изотермическое движение двух несмешивающихся жидкостей в пороупругой среде // Известия Алтайского государственного университета. 2015. № 1-2. С. 131-135. https://doi.org/10.1425izvasu(2015)1.2-24
Connolly J.A.D., Podladchikov Y.Y. Compaction-Driv Fluid Flow in Viscoelasticrock // Geodinamica Acta. 1998. Vol. 11. P. 55-84. https://doi.org/10.1016/S0985-3111(98)80006-5
Антонцев С.Н., Кажихов А.В., Монахов В.Н. Краевые задачи механики неоднородных жидкостей. Новосибирск: Изд-во «Наука». 1983. С. 315.
Гилев П.В., Папин А.А. Фильтрация двух несмешивающихся несжимаемых жидкостей в тонком пороупру-гом слое // Сибирский журнал индустриальной математики. 2024. Т. 27. № 2. С. 20-33. https://doi.org/10.33048/SIBJIM.2024.27.202
Бочаров О.Б., Монахов В.Н. Неизотермическая фильтрация несмешивающихся жидкостей с переменным остаточным насыщением // Динамика сплошной среды. 1988. Т. 88. С. 3-11.
Бочаров О.Б., Монахов В.Н. Краевые задачи неизотермической двухфазной фильтрации в пористых средах // Динамика сплошной среды. 1988. Т. 86. С. 47-59.
Токарева М.А., Вирц Р.А., Ларионова В.Н. Математическая модель движения жидкости в пороупругом льду с учетом фазовых переходов и движения льда // Труды семинара по геометрии и математическому моделированию. 2021. № 7. С. 44-49. https://doi.org/10.17516/1997-1397-2020-13-6-763-773
Сибин А.Н., Папин А.А. Тепломассоперенос в тающем снеге // Прикладная механика и техническая физика. 2021. Т. 62. № 1. С. 109-118. https://doi.org/10.15372/PMTF20210112
Блохин А.М., Доровский В.Н. Проблемы математического моделирования в теории многоскоростного континуума. Новосибирск: Изд-во СО РАН. 1994. С. 184.
Jardani A., Revil A. Seismoelectric Couplings in a Po-roelastic Material Containing Two Immiscible Fluid Phases // Geophysical Journal International. 2015. Vol. 202. No 2. P. 850-870. https://doi.org/10.1093/gji/ggv176
Shelukhin V.V. A Poroelastic Medium Saturated by a Two-Phase Capillary Fluid // Continuum Mechanics and Thermodynamics. 2014. Vol. 26. No 5. P. 619-638. https:// doi.org/10.1007/s00161-013-0321-x
Chengwei Z., Chong P., Wei W, Chun W. A MultiLayer SPH Method for Generic Water-Soil Dynamic Coupling Problems. Part I: Revisit, Theory and Validation // Computer Methods in Applied Mechanics and Engineering. 2022. Vol. 396. https://doi.org/10.1016/jxma.2022.115106
Copyright (c) 2026 Павел Вячеславович Гилев, Александр Алексеевич Папин
This work is licensed under a Creative Commons Attribution 4.0 International License.
Izvestiya of Altai State University is a golden publisher, as we allow self-archiving, but most importantly we are fully transparent about your rights.
Authors may present and discuss their findings ahead of publication: at biological or scientific conferences, on preprint servers, in public databases, and in blogs, wikis, tweets, and other informal communication channels.
Izvestiya of Altai State University allows authors to deposit manuscripts (currently under review or those for intended submission to Izvestiya of Altai State University) in non-commercial, pre-print servers such as ArXiv.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
